A An argument against Bohmian mechanics?

[PeterDonis]

Do you mean the physics don't have math content?

No. I'm just trying to figure out which math content you are referring to when you talk about "no FTL signaling".

I explained in #368 how the math content of realism as reflected in the Bell inequalities bears on the observability of FTL

As far as I can tell, you are just pasting the labels "local", "nonlocal", "realist", "nonrealist" in various places but never actually saying what, physically, you think is observable or not observable.

Testing for FTL signaling is simple: send the same information in an ordinary light signal and in whatever other kind of signal you are trying to test for FTL signaling. If the information can be extracted from the latter signal at the receiver before the ordinary light signal arrives, you have FTL signaling; if not, not. EPR-type experiments test negative for FTL signaling by this criterion, because the full information contained in the correlations between measurement results is not available at either location until the result from the other location has been communicated by an ordinary light signal (or, in practice, something slower).

Testing for violations of the Bell inequalities is also simple; I don't think I need to elaborate on that here.

What else is there to test?

 

[zonde]

This was also my point in #283. The distinction local versus nonlocal has no empirical or operational meaning for classical realistic(i.e. hidden variables) theories because one can either consider they have nonlocal implicit influence(but no way to observe FTL signaling) as you say or if one decides the theory is local by the independent construction of the hidden variables there is no way to design an experiment to show this as it would be require the use of an instantaneous measure of spacelike separated events(i.e. FTL signaling) to do it, which is a strange way for a theory to be local .

Why do you think that experiment would need "instantaneous measure of spacelike separated events" to tell apart nonlocal implicit influence and local hidden variables? The only reason I could imagine would be that you take measurements as non factual (the MWI way).
And just to make sure that we are on the same page I would like to ask if you are familiar with this very simple counterexample type of Bell inequality: https://www.physicsforums.com/threads/a-simple-proof-of-bells-theorem.417173/#post-2817138

 

[Demystifier]

The above considerations show that we cannot hope for this unless quantum mechanics is incorrect.

Such a theory cannot make the same predictions as quantum mechanics.

You can of course leave this possibility open, but then you must propose a theory that disagrees with quantum mechanical predictions.

Well, QM and the theory I am talking about have the "same" predictions only in the FAPP (For All Practical Purposes) sense. In principle they differ, but in practice they do not.

Loosely speaking, this is like comparing thermodynamics with statistical physics. In thermodynamics the second law $dS\ge 0$ is an exact law. In statistical physics a deviation from $dS\ge 0$ is possible, but the probability for such a deviation is so small that it can be neglected FAPP. Bohmian mechanics (either minimal or non-minimal) is for QM what Boltzmann classical statistical mechanics was for thermodynamics at the end of 19th century. At that time atoms were "hidden variables" and Mach criticized Boltzmann's statistical mechanics for basing the theory on unobserved atoms. Boltzmann was so depressed by the fact that the mainstream physicists did not accept his theory that he eventually committed suicide. I think that's a very important lesson from the history of science.

 

[RockyMarciano]

As far as I can tell, you are just pasting the labels "local", "nonlocal", "realist", "nonrealist" in various places but never actually saying what, physically, you think is observable or not observable.

Then why do you avoid quoting the next sentences of my post where I actually explain what, physically, I say is not observable(I only spoke about non observability, that is about claims without physical content). I'll repeat it, the first case(non observability of FTL signaling in realist theories that claim FTL influence is explained by Demystifier in #141 so I guess is clear enough. The second case I explained is the non empirical content of claiming that a realist theory doesn't allow FTL influence. The reason that is claimed for a so called "local hidden variables" theory is that the assumption is made that a realist theory has predetermined values for all possible measurement outcomes, but this assumption could only be validated in practice by designing an experiment that performed simultaneous measurements in spacelike separated points. and such an experiment requires FTL signaling.
I guess if you quote this post cleverly enough again you can claim once more that I never actually explained what I think is not observable for realist theories, but again why would you do it?

 

[stevendaryl]

Sure, they just measure the x component of the spin. What I described, is what's usually called "collapse", i.e., the preparation of an observable to have a determined value by filtering, which indeed means just to block all the unwanted states.

The whole point of EPR was to distinguish between the quantum collapse from various of the unproblematic variants.

 

[RockyMarciano]

Why do you think that experiment would need "instantaneous measure of spacelike separated events" to tell apart nonlocal implicit influence and local hidden variables?

No, not to tell apart, there is no experiments to tell apart the claim of "FTL influence" from "non FTL influence" for hidden variables theory if in those theories those claims have no empirical content.
I said that the claim of "no FTL influence" in a hidden variables theory would need "instantaneous measure of spacelike separated events" to be substantiated, because the claim is made based on the assumption of independence of the hidden variables at each spacelike separated point, in other words that the values of all possible measurement results are predetermined, and the only way to test this predetermination in principle is by an experiment that measures spacelike separated events instantaneously(so one can verify the predetermination of results for all possible measurements at any point) and that would require FTL signaling.
I really don't think this is so difficult to see, one just have to acknowledge that hidden variable theories assume the classical galilean relativity with infinite speed of propagation of information and if you think about it that is the only way they can ensure a claim about non influence of one measurement on the rest of measurements separated spatially necessary for the hidden variables to determine measurement outcomes.

The only reason I could imagine would be that you take measurements as non factual (the MWI way).

Nothing to do with this. See above.

And just to make sure that we are on the same page I would like to ask if you are familiar with this very simple counterexample type of Bell inequality: https://www.physicsforums.com/threads/a-simple-proof-of-bells-theorem.417173/#post-2817138

Sure but I'm afraid they are using the term nonlocal there to mean what in the Nature paper I linked called local nonrealist.

 

[stevendaryl]

I can't quite follow this,( but I'm trying my best). If the electron were in a superposition of u and d states wouldn't it have needed to have been prepared in a definite state of l or r to be guaranteed to produce a random result in the u/d direction? If the up coefficient were bigger than the down coefficient (so to speak) would it not be expected to migrate one way rather than the other?

Sorry for not responding to this sooner. In the EPR experiment, Alice and Bob each have probability exactly 1/2 of measuring spin-up along whatever direction they choose to measure spins. The mathematical explanation is that neither Alice's nor Bob's particle is in a superposition, but the two-particle composite system is in the state \frac{1}{\sqrt{2}} (|u\rangle |d\rangle - |d\rangle |u\rangle).

I'm not sure if that answers your question...

 

[zonde]

I said that the claim of "no FTL influence" in a hidden variables theory would need "instantaneous measure of spacelike separated events" to be substantiated, because the claim is made based on the assumption of independence of the hidden variables at each spacelike separated point, in other words that the values of all possible measurement results are predetermined, and the only way to test this predetermination in principle is by an experiment that measures spacelike separated events instantaneously(so one can verify the predetermination of results for all possible measurements at any point) and that would require FTL signaling.

You are mixing theory with reality. A theory is what we put into it. There is no hidden content. If a theory says that such and such phenomena is explained by such and such mathematical model (plus correspondence rules) then that's all about it. And we test the theory by verifying it's predictions. We can't prove that some theory is universally valid for any conceivable measurement.

 

[Demystifier]

@stevendaryl are you now satisfied with #371?

 

[stevendaryl]

@stevendaryl are you now satisfied with #371?

I'm still a little confused about Bohmian mechanics and probabilities, in the case of spin-1/2.

Empirically, we have the following situation:

1. You prepare a beam of electrons and filter out only those that are spin-up in the direction \hat{a} (by sending them through a Stern-Gerlach device and only considering those that deflect in a particular direction).
   
2. You perform a second filtering, and filter out those that are spin-up in the direction \hat{b}.
3. The fraction of those who pass both filters is given by: cos^2(\frac{\theta}{2}) where \theta is the angle between \hat{a} and \hat{b}. This can also be written, using a trigonometric identity as: \frac{1}{2}(1+cos(\theta)) = \frac{1}{2}(1+ \hat{a} \cdot \hat{b}), if \hat{a} and \hat{b} are unit vectors.

Now, we try to explain this using a local deterministic hidden-variable theory (we'll get to the nonlocal version in a moment). That means we assume that there is a variable \lambda attached to each electron, and it's value is distributed according to some probability distribution P(\lambda), and this variable determines whether the electron passes the second filter. Then to agree with predictions, the set V_{\hat{b}} of all values of \lambda such that the electron will pass the second filter must have a measure equal to \frac{1}{2}(1+ \hat{a} \cdot \hat{b}). We can go through a Bell-type argument to show that there is no probability distribution P(\lambda) that can simultaneously give this measure to each set V_{\hat{b}} for all possible values of \hat{b}. (We can actually do better than that, and find three values of \hat{b}, and prove that there is no probability distribution that works for those three values.)

So my question is: how does allowing nonlocal interactions change this story? I think I just need to work this out myself. Presumably, allowing nonlocal interactions makes the problems of the impossible probability distribution disappear, but at the moment, I'm not sure I can put together why.

 

[Demystifier]

I'm still a little confused about Bohmian mechanics and probabilities, in the case of spin-1/2.

Empirically, we have the following situation:

1. You prepare a beam of electrons and filter out only those that are spin-up in the direction \hat{a} (by sending them through a Stern-Gerlach device and only considering those that deflect in a particular direction).
   
2. You perform a second filtering, and filter out those that are spin-up in the direction \hat{b}.
3. The fraction of those who pass both filters is given by: cos^2(\frac{\theta}{2}) where \theta is the angle between \hat{a} and \hat{b}. This can also be written, using a trigonometric identity as: \frac{1}{2}(1+cos(\theta)) = \frac{1}{2}(1+ \hat{a} \cdot \hat{b}), if \hat{a} and \hat{b} are unit vectors.

Now, we try to explain this using a local deterministic hidden-variable theory (we'll get to the nonlocal version in a moment). That means we assume that there is a variable \lambda attached to each electron, and it's value is distributed according to some probability distribution P(\lambda), and this variable determines whether the electron passes the second filter. Then to agree with predictions, the set V_{\hat{b}} of all values of \lambda such that the electron will pass the second filter must have a measure equal to \frac{1}{2}(1+ \hat{a} \cdot \hat{b}). We can go through a Bell-type argument to show that there is no probability distribution P(\lambda) that can simultaneously give this measure to each set V_{\hat{b}} for all possible values of \hat{b}. (We can actually do better than that, and find three values of \hat{b}, and prove that there is no probability distribution that works for those three values.)

So my question is: how does allowing nonlocal interactions change this story? I think I just need to work this out myself. Presumably, allowing nonlocal interactions makes the problems of the impossible probability distribution disappear, but at the moment, I'm not sure I can put together why.

In this example there is no entanglement and therefore there is no need for non-local hidden variables. Indeed, the Bohmian description of this case is local. What you call "Bell-type argument" above, should really be a Kochen-Specker type argument. In other words, the non-trivial property of hidden variables we need here is contextuality, not non-locality. The notion of Bell non-locality includes also contextuality, but the converse is not true; contextuality does not necessarily include Bell non-locality. Contextuality means that your $P(\lambda)$ changes when the experimental setup changes. But it is local, in the sense that this change can be described by a local hidden variable theory.

 

[zonde]

Nope. Bohmian mechanics is an explicit counterexample: each individual trajectory is deterministic, but its equation of motion includes the quantum potential, which is what allows it to violate the Bell inequalities (because the quantum potential leads to the QM prediction for joint probabilities of measurement results, which is not factorizable).

I suppose I could get some understanding by comparing two conditional wavefunctions of electron form entangled pair where the spin of other electron is already measured along $\vec a_y$ or $\vec a_z$. Simpler explanations (like wikipedia or this Goldstein's article) of BM give only explanations for spinless conditional wavefunctions. Anyways measurement of remote entangled electron shouldn't change configuration (position) of the first electron directly. Any change is only trough (conditional) wavefunction, as it seems to me.

Bell explicitly discussed this exact point.

Is this Bell's explanation in book? Or maybe there is some online link?

 

[stevendaryl]

In this example there is no entanglement and therefore there is no need for non-local hidden variables. Indeed, the Bohmian description of this case is local. What you call "Bell-type argument" above, should really be a Kochen-Specker type argument.

Well, the Bell argument "factors" into two different arguments:

1. The perfect correlations/anti-correlations between distant pairs implies (under the assumption of local realism) that there is a variable \lambda that deterministically decides the outcome of every possible spin measurement.
2. Given #1, the problem becomes to come up with a function A_{\alpha, \lambda} that returns \pm 1 for every value of \lambda and which has the correct statistics.

The second problem is no different, depending on whether you're dealing with entangled pairs or just trying to explain the result of measurements of a single electron.

In other words, the non-trivial property of hidden variables we need here is contextuality, not non-locality. The notion of Bell non-locality includes also contextuality, but the converse is not true; contextuality does not necessarily include Bell non-locality. Contextuality means that your $P(\lambda)$ changes when the experimental setup changes. But it is local, in the sense that this change can be described by a local hidden variable theory.

Yes, a single experiment can easily be explained using hidden variables, but we are only interested in those explanations that can be extended to the twin-pair problem. It's no use to come up with an explanation that we know (from other information) is false.

But what I'm asking for is how allowing contextuality changes the mathematics. What's an example of a contextual explanation?

 

[Demystifier]

What's an example of a contextual explanation?

Bohmian mechanics. To show that BM leads to the same measurable predictions as standard QM, BM needs to take into account the wave function of the measuring apparatus (WFMA). (Standard QM can also take into account the same WFMA, but with some Copenhagen-like doctrine the predictions of standard QM can be obtained even without WFMA.) This WFMA depends on the measurement setup, which makes it contextual. The motion of Bohmian particles also depends on this wave function, so contextuality at the level of wave functions translates into contextuality of particle trajectories.

 

[stevendaryl]

Bohmian mechanics.

I guess what I was asking for was something more abstract. In terms of the hidden-variables story that I gave, how do things get modified by allowing contextual or nonlocal measurements? Presumably, there is still a \lambda, and there is still a probability distribution on \lambda. So what gets modified?

 

[Demystifier]

I guess what I was asking for was something more abstract. In terms of the hidden-variables story that I gave, how do things get modified by allowing contextual or nonlocal measurements? Presumably, there is still a \lambda, and there is still a probability distribution on \lambda. So what gets modified?

When the measurement setup is changed, then it is $P(\lambda)$ that gets modified.

 

[stevendaryl]

When the measurement setup is changed, then it is $P(\lambda)$ that gets modified.

That doesn't seem right. \lambda is a variable permanently associated with each electron (in Bohmian mechanics, it would be the position of the electron at some reference time, t_0). So the values of \lambda are chosen before the choice of the detector setting. Maybe the sets V_{\hat{b}} are changed when you change the detector settings?

 

[RockyMarciano]

... We can't prove that some theory is universally valid for any conceivable measurement.

I'm not sure I understand what you posted but it seems you missed my point, I'm saying that there should be falsifiable content in a theory, in other word the physical claims of a theory should be testable in principle, if a hidden variables theory claims to allow or not allow FTL influences that should be testable or it has no meaning in addition to having hidden variables determining the measurement outcomes. This has nothing to do with proving anything, physical theories are not proven, just confirmed until empirical info discards them, but first it must have empirically testable meaning for its claims at least in principle, or else those claims are scientifically meaningless.

 

[RockyMarciano]

I guess what I was asking for was something more abstract. In terms of the hidden-variables story that I gave, how do things get modified by allowing contextual or nonlocal measurements? Presumably, there is still a \lambda, and there is still a probability distribution on \lambda. So what gets modified?

I think my #393 could help here, quantum contextuality is basically the way some hidden variables interpretations of QM get around the contradiction between their deterministic nature and the non-deterministic nature imposed on QM by the Born rule, otherwise they wouldn't have the same results and couldn't claim to be just an interpretation.
To answer your question nothing gets modified mathematically by contextuality, just the end result, the classical probabilities of deterministic theories are switched in an ad hoc way by the non-deterministic probabilities produced by the Born rule(contradicitng all the mathematical arguments associated to hidden variables and the deterministic narrative). I would say for anyone except the proponents of such interpretations the arbitrariness should be more than evident.
It is just a way to circunvent the Kochen-Specker theorem by introducing the caveat that the hidden variables can behave for predictions as dictated by QM's Born rule postulate

 

[RockyMarciano]

That doesn't seem right. \lambda is a variable permanently associated with each electron (in Bohmian mechanics, it would be the position of the electron at some reference time, t_0). So the values of \lambda are chosen before the choice of the detector setting. Maybe the sets V_{\hat{b}} are changed when you change the detector settings?

But note that when they are allowed to change depending on context(detector settings), that is no longer a hidden variables model.

 

[PeterDonis]

the next sentences of my post where I actually explain what, physically, I say is not observable

No, you don't, because you're not giving the word "realist" any precise mathematical meaning. (At first you didn't give the word "local" any precise mathematical meaning either, but I think it's established now that for you that means "no FTL signaling", which can be precisely defined mathematically.)

 

[PeterDonis]

Is this Bell's explanation in book?

It's in one of his original papers, which are published in Speakable and Unspeakable in Quantum Mechanics. I don't have any links handy to online versions.

 

[zonde]

I'm not sure I understand what you posted but it seems you missed my point, I'm saying that there should be falsifiable content in a theory, in other word the physical claims of a theory should be testable in principle, if a hidden variables theory claims to allow or not allow FTL influences that should be testable or it has no meaning in addition to having hidden variables determining the measurement outcomes.

Yes, there should be falsifiable content predictions in a theory. But I would not say there are claims in the theory, there are predictions and there are assumptions. Assumptions are indirectly tested by checking that reality is consistent with predictions of the theory.
Hidden variables theory without FTL influences obey Bell inequalities. That's prediction that can tell apart two types of hidden variables theories as hidden variables theory with FTL influences can violate Bell inequalities.

 

[Jilang]

Sorry for not responding to this sooner. In the EPR experiment, Alice and Bob each have probability exactly 1/2 of measuring spin-up along whatever direction they choose to measure spins. The mathematical explanation is that neither Alice's nor Bob's particle is in a superposition, but the two-particle composite system is in the state \frac{1}{\sqrt{2}} (|u\rangle |d\rangle - |d\rangle |u\rangle).

I'm not sure if that answers your question...

Is this just not a result of ignorance of which particle of the pair you have and also which pair you have? Two levels of ignorance, so to speak.

 

[RockyMarciano]

No, you don't, because you're not giving the word "realist" any precise mathematical meaning.

Maybe you missed it but I defined several times what I(and many others) call realist, even quoted explicitly the definition from the Nature paper I linked. If you mean that you don't know what the math content of such definition is just say so and I'll provide it, but I would think everyone at this point knows what the math content of classical deterministic theories with hidden parameters is.
I'm still puzzled by your questions. do you read my answers?

 

[stevendaryl]

Is this just not a result of ignorance of which particle of the pair you have and also which pair you have? Two levels of ignorance, so to speak.

I think you can distinguish which particle without destroying the entanglement. If there is an electric field, for instance, the positron will drift in one direction and the electron will drift in the other.

 

[RockyMarciano]

Hidden variables theory without FTL influences obey Bell inequalities. That's prediction that can tell apart two types of hidden variables theories as hidden variables theory with FTL influences can violate Bell inequalities.

The distinction between assumptions and predictions is fine, but you are not applying it here. The assumption of FTL influences being possible or not in hidden variables theories is not a prediction: in the case when it is assumed there are FTL influences like in the Bohmian interpretations, it is not predicted that FTL signaling is possible, do you agree?(see post #141 if you are doubtfult).
And in the case where it is assumed there are no FTL influences (so called "local hidden variables") actually its math content assumes galilean invariance (i. e. is compatible with infinite propagation velocity like in classical deterministic theories like classical mechanics and like NRQM but NRQM is not hidden variables-aka realist, aka classical deterministic and thus its predictions violate Bell inequalities), there is no constant finite speed limit, so it can't actually predict "no FTL signaling" according to its math content. Do you not agree with this?
So what violations of BI tell apart is classical deterministic hidden variables theories from non-hidden variables theories.

 

[RockyMarciano]

@stevendaryl I''m actually also curious if you agree with anything I wrote in my previous post, and if not where you think I'm wrong.

 

[stevendaryl]

@stevendaryl I''m actually also curious if you agree with anything I wrote in my previous post, and if not where you think I'm wrong.

Which one? The one that starts "The distinction between assumptions and predictions is fine..."

 

[PeterDonis]

If you mean that you don't know what the math content of such definition is just say so and I'll provide it

That would be helpful.

 

[Demystifier]

\lambda is a variable permanently associated with each electron (in Bohmian mechanics, it would be the position of the electron at some reference time, t_0).

No. In Bohmian mechanics, \lambda are the positions (at t_0) of all particles relevant for the experiment. This includes the position of that electron, as well as positions of all particles constituting the measuring apparatus.

In fact, to understand why BM leads to the same measurable predictions as standard QM, the apparatus positions are much more important than the electron position. See
https://arxiv.org/abs/1112.2034

 

[zonde]

No. In Bohmian mechanics, \lambda are the positions (at t_0) of all particles relevant for the experiment. This includes the position of that electron, as well as positions of all particles constituting the measuring apparatus.

Does $\lambda$ have to include positions for particles of random number generator that will determine if measurement apparatus will be rotated/not rotated right before measurement in order to make correct predictions?

EDIT: Obviously you can't make prediction without output of random number generator. So the question should be if it's possible to make two conditional predictions based on output of RND.

 

[zonde]

The distinction between assumptions and predictions is fine, but you are not applying it here. The assumption of FTL influences being possible or not in hidden variables theories is not a prediction: in the case when it is assumed there are FTL influences like in the Bohmian interpretations, it is not predicted that FTL signaling is possible, do you agree?(see post #141 if you are doubtfult).
And in the case where it is assumed there are no FTL influences (so called "local hidden variables") actually its math content assumes galilean invariance (i. e. is compatible with infinite propagation velocity like in classical deterministic theories like classical mechanics and like NRQM but NRQM is not hidden variables-aka realist, aka classical deterministic and thus its predictions violate Bell inequalities), there is no constant finite speed limit, so it can't actually predict "no FTL signaling" according to its math content. Do you not agree with this?

"no FTL signaling" is not a valid prediction. Valid prediction is that particular phenomena have such and such properties that it can't be used to get FTL signaling.

So what violations of BI tell apart is classical deterministic hidden variables theories from non-hidden variables theories.

I don't see how this follows from what you said.

 

[stevendaryl]

No. In Bohmian mechanics, \lambda are the positions (at t_0) of all particles relevant for the experiment. This includes the position of that electron, as well as positions of all particles constituting the measuring apparatus.

Ah! Thanks.

 

[Demystifier]

Does λ have to include positions for particles of random number generator that will determine if measurement apparatus will be rotated/not rotated right before measurement in order to make correct predictions?

Yes, except with the caveat that it is really a pseudo-random number generator.

 

[Gan_HOPE326]

Sorry for jumping in without having read the full 22-pages thread but just excerpts of it, but this is a topic I'm dearly interested in as I find Bohmian mechanics pretty fascinating, if only because it provides a very useful way to visualise otherwise pretty alien concepts. The paper linked from the OP seems to me to fail the way Demystifier pointed out: it relies on expectation values for correlations $x(t)x(0)$, ignoring that this is not what experiments actually measure. If I were to measure $x(0)$ then I'd alter the wavefunction depending on the uncertainty on position given by my apparatus, and any successive time evolution would have to start not with the groundstate but with a function centred around the measured value. Ideally, if I measured it with infinite precision it'd be a delta function, with no knowledge at all about the momentum of the particle. Such a function would of course contain a lot of high-energy modes from the oscillator, therefore the connected Bohmian particle would move, as it happens in mixed states.

I'd also like to point out this paper that I've been working with since it's interesting for me from a computational point of view:

http://journals.aps.org/prx/abstract/10.1103/PhysRevX.4.041013

This "Many Interacting World" interpretation rewrites Bohmian mechanics by doing away with the wavefunction altogether, or rather, using it as a 'regular' field that generates a (functionally pretty complex) force between copies of the same particles across 'worlds'. In this way the problem of the unidirectional effect of the wavefunction on the particle is solved: if we consider all the particle's copies, when A acts on B, B acts on A equally. I'm not really much into exploring the philosophical implications of such an interpretation or whether it counts as 'real', but I think it's a perhaps more easily acceptable way to look at Bohmian mechanics since it makes it much less 'alien' compared to other classical systems.

 

[RockyMarciano]

I don't see how this follows from what you said.

Easy, if neither local nor nonlocal hidden variables theories are capable of producing verifiable predictions about FTL signaling(do you agree with this?, if not give some example), even if they have different assumptions about FTL influence, they are equivalent as theories, they could be only considered as different interpretations of the same hidden variables theories that is put in mathematical terms in the Bell inequalities.

The same situation happens with the different interpretations of QM, all being the same theory even if their assumptions are contradictory.
So the value of experiments violating the BI can be interpreted as rejecting deterministic hidden variable theories, and I say only theories, because for instance interpretations of QM are of course not affected as long as they don't claim themselves to be independent theories.

 

[RockyMarciano]

Which one? The one that starts "The distinction between assumptions and predictions is fine..."

I think my point is clearer in #437.

 

[PeterDonis]

if neither local nor nonlocal hidden variables theories are capable of producing verifiable predictions about FTL signaling(do you agree with this?, if not give some example), even if they have different assumptions about FTL influence, they are equivalent as theories

Huh? On your definition of "local", there is no such thing as a "nonlocal hidden variable theory", because all of them agree that FTL signaling is impossible. So what you should be saying here is simply that by your definition, there are no nonlocal hidden variable theories, period. You should not be saying anything about the predictions that nonlocal hidden variable theories make, because by your definition there are no such theories.

On Bell's definition of "nonlocal", where it means "violates the Bell inequalities", then it is meaningful to talk about the predictions of nonlocal hidden variable theories. But by definition, those are distinguishable as theories from local hidden variable theories, since the latter satisfy the Bell inequalities. The fact that both agree that FTL signaling is impossible does not make them equivalent as theories, since the Bell inequalities can be tested experimentally.

 

[RockyMarciano]

Huh? On your definition of "local", there is no such thing as a "nonlocal hidden variable theory", because all of them agree that FTL signaling is impossible. So what you should be saying here is simply that by your definition, there are no nonlocal hidden variable theories, period. You should not be saying anything about the predictions that nonlocal hidden variable theories make, because by your definition there are no such theories.

But I explained how my definition of local(and of nonlocal) has no empirical content when applied to hidden varaible theories. If I gave predictive value to "local" you would be right. But I showed how it doesn't have predictive value. Otherwise it should be easy to show how local or non local hiddenvariables predict FTL signaling/no signaling. The nonlocal case is clear enough, do you think local hidden variables predict "no FTL signaling"? Then violation of the inequalities should convince you FTL signaling is possible. Does it?

On Bell's definition of "nonlocal", where it means "violates the Bell inequalities", then it is meaningful to talk about the predictions of nonlocal hidden variable theories. But by definition, those are distinguishable as theories from local hidden variable theories, since the latter satisfy the Bell inequalities. The fact that both agree that FTL signaling is impossible does not make them equivalent as theories, since the Bell inequalities can be tested experimentally.

I agree if one defines nonlocal as "violates the Bell inequalities", but this cause all kind of confusion, even more if as I said it can be shown that for hidden variable theories local/nonlocal can be seen as different interpretations of the same hidden variable theory(much as it happens with QM interpretations). Then the test of the inequalities gives a clear way to reject hidden variables altogether.

 

[PeterDonis]

I explained how my definition of local(and of nonlocal) has no empirical content

Which makes no sense to me since FTL signaling is something that is straightforward to test for. So testing whether a theory's predictions are "local" (no FTL signaling) or "nonlocal" (allows FTL signaling) is straightforward. And by that definition, all theories we currently know of are local. There are no nonlocal theories.

when applied to hidden varaible theories

I don't see how this matters at all. There are no nonlocal hidden variable theories by your definition, but there are no nonlocal non-hidden-variable theories by your definition either. (At least, none that have not been ruled out by experiment.) Hidden variables are simply irrelevant to local/nonlocal by your definition.

I showed how it doesn't have predictive value

You did no such thing. You did the opposite, by defining "local" and "nonlocal" in terms of FTL signaling, which obviously has direct predictive value since it can be directly tested.

Otherwise it should be easy to show how local or non local hiddenvariables predict FTL signaling/no signaling.

You don't even appear to understand your own definition. Once again: by your definition, there are no nonlocal theories. Hidden variable/no hidden variable is irrelevant. You can't even "show" anything about what "nonlocal hidden variables" predict until you have a theory to use to do the predicting. There isn't one.

Of course there are hidden variable theories that predict violations of the Bell inequalities, but you have explicitly said that is not the definition of "nonlocal" you want to use. And yet you keep talking as if there are "nonlocal" theories that we can discuss. There aren't.

for hidden variable theories local/nonlocal can be seen as different interpretations of the same hidden variable theory

Are you reading what you write? You are saying here, if we use your definition of "local" and "nonlocal", that theories that predict no FTL signaling, and theories that predict FTL signaling is allowed, "can be seen as different interpretations of the same hidden variable theory". That is obviously self-contradictory since the predictions differ for a direct observable.

 

[RockyMarciano]

A condition to understand what I wrote is the following: I've made a clear and reasoned distinction between the definitions "doesn't/does allow FTL communication" as assumptions(not predictions) in a theory in which they can't be verified by construction of the theory, and the definitions in other contexts where they can be given a testable meaning easily. Of course for anyone not being able to grasp this distinction or that ignores the arguments I gave for it will find incomprehensible what I wrote.

 

[RockyMarciano]

Example:Bohmian mechanics assumes, but doesn't predict "FTL communication". If it predicted it , it woulnd't be an interpretation of QM.

 

[PeterDonis]

the definitions "doesn't/does allow FTL communication" as assumption in a theory in which they can't be verified by construction of the theory

And this definition means nothing to me, because I don't care about it. I care about the testable definition, since that's the one that has obvious physical meaning. Basically you're making up your own definition of something and then arguing that it's not verifiable. You may be right, but so what?

 

[RockyMarciano]

And this definition means nothing to me, because I don't care about it. I care about the testable definition, since that's the one that has obvious physical meaning. Basically you're making up your own definition of something and then arguing that it's not verifiable. You may be right, but so what?

I justified why I consider local/nonlocal not to have predicitive value in a hidden variables theory(if you think it does have tell me how and you may convince me). I think it helps to clarify how experiments showing violations of Bell's inequalities should be interpreted. Similarly different interpretations of QM with a lot of assumptions with no predictive value, some of them quite outrageous serve for some to clarify the meaning of QM wheter one cares for those weird assumptions or not.

 

[PeterDonis]

I justified why I consider local/nonlocal not to have predicitive value in a hidden variables theory

I'm sorry, I can't even understand why anyone should care about your definitions so what you think of as a justification I see as meaningless.

 

[RockyMarciano]

Hmm, I think you are not seeing the difference between assumptions and predictions. In any case my definitions are taken from the paper I linked. It's simply that they don't have predictive value in the context of deterministic hidden variables theories. Take Galilean relativity, even if compatible with no constant finite speed, it doesn't actually predict FTL signaling, but it also assumes local action as separability of inertial frames and yet it doesn't predict "no FTL signaling" either.

 

[PeterDonis]

I think you are not seeing the difference between assumptions and predictions.

I think you are insisting on using words in a very unusual and idiosyncratic way, and then wondering why what you say doesn't make sense to others.

Take Galilean relativity, even if compatible with no constant finite speed, it doesn't actually predict FTL signaling, but it also assumes local action as separability of inertial frames and yet it doesn't predict "no FTL signaling" either.

I don't understand what all this means, except for "no constant finite speed". The way I would describe Galilean relativity, as opposed to SR, is that Galilean relativity allows instantaneous causality--two events can be causally connected regardless of their separation in space as compared to their separation in time (the latter can even be zero). But Galilean relativity is perfectly compatible with light having a finite speed; it just won't be a finite invariant speed, it will vary depending on the observer's state of motion relative to the source.

 

[zonde]

Easy, if neither local nor nonlocal hidden variables theories are capable of producing verifiable predictions about FTL signaling(do you agree with this?, if not give some example),

I agree.

even if they have different assumptions about FTL influence, they are equivalent as theories, they could be only considered as different interpretations of the same hidden variables theories that is put in mathematical terms in the Bell inequalities.

Two theories do not have to produce different predictions for any test. Different theories can agree about some prediction but disagree about other predictions. Bell inequality violations can be experimentally tested and that's enough to say that they are different theories rather than just interpretations.

 

[RockyMarciano]

I agree.

Two theories do not have to produce different predictions for any test. Different theories can agree about some prediction but disagree about other predictions. Bell inequality violations can be experimentally tested and that's enough to say that they are different theories rather than just interpretations.

They don't have to do it for any test, but I'm only referring to one specific test, the one that bears on the distinction local/nonlocal. So of course the experimental test of BI's violations is enough to tell apart deterministic hidden variables theories from non-deterministic(nonhidden variables) theories and that's what it does. In many books and papers they call this telling apart local and nonlocal theories(like in the example you linked), because they use "local" to mean deterministic hidden variables which causes further confusion.

One very clear example of the confusion is that Bohmian mechanics is an interpretation that is deterministic hidden variables but as a theory it must follow QM predictions that are non-deterministic as confirmed by experiment, so it is actually a non-deterministic non-hidden variables theory with deterministic hidden variables interpretation. The word "schizofrenic" mentioned in previous posts could define this situation.